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# If x is a positive integer, is 6 a factor of x? 1) 6 is a factor of 3x

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Joined: 14 Nov 2016
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If x is a positive integer, is 6 a factor of x? 1) 6 is a factor of 3x [#permalink]

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Updated on: 11 Apr 2017, 20:32
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Difficulty:

35% (medium)

Question Stats:

70% (01:25) correct 30% (01:10) wrong based on 98 sessions

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If x is a positive integer, is '6' a factor of x?

1) 6 is a factor of 3x
2) 12 is a factor of $$x^2$$

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Originally posted by hazelnut on 24 Mar 2017, 05:54.
Last edited by Vyshak on 11 Apr 2017, 20:32, edited 1 time in total.
Edited the question
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Re: If x is a positive integer, is 6 a factor of x? 1) 6 is a factor of 3x [#permalink]

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24 Mar 2017, 08:45
1
1
ziyuen wrote:
If x is a positive integer, is 6a factor of x?

1) 6 is a factor of 3x
2) 12 is a factor of $$x^2$$

It seems you've got unlimited source of good questions.

1) 6 is a factor of 3x

$$3x = 6y$$

$$x = 2y$$

$$x=2n$$, $$y=n$$, where $$n$$ is any integer. $$x$$ may or may not be a multiple of $$6$$. Insufficient.

2) 12 is a factor of $$x^2$$

$$x^2 = 12y$$

$$x = \sqrt{12y} = 2*\sqrt{3y}$$.

For $$x$$ to be an integer min value of $$y$$ should be $$3$$, hence min value of $$x=6$$. Sufficient.

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Re: If x is a positive integer, is 6 a factor of x? 1) 6 is a factor of 3x [#permalink]

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11 Apr 2017, 15:24
I don't agree with the OA...
is 6a factor of x?
we are given 0 information about a.
a can be infinite - so how 6*a is a factor of x?

otherwise, if we are not asked for 6a where a is a coefficient - edit the question, as it creates confusion
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Joined: 12 Sep 2015
Posts: 2559
Re: If x is a positive integer, is 6 a factor of x? 1) 6 is a factor of 3x [#permalink]

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11 Apr 2017, 15:38
Top Contributor
mvictor wrote:
I don't agree with the OA...
is 6a factor of x?
we are given 0 information about a.
a can be infinite - so how 6*a is a factor of x?

otherwise, if we are not asked for 6a where a is a coefficient - edit the question, as it creates confusion

There's a typo on the OP.
"6a" should be "6 a"

I originally read it as "6a" also.

Cheers,
Brent
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Re: If x is a positive integer, is 6 a factor of x? 1) 6 is a factor of 3x [#permalink]

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15 Apr 2017, 22:32
1) x can be = 2,4,6,8 ... not sufficient
2) since x^2 could be = 12, 24,36,48,60 there are only a few combinations when x is integer => then 6 is definitely a factor of x
Re: If x is a positive integer, is 6 a factor of x? 1) 6 is a factor of 3x   [#permalink] 15 Apr 2017, 22:32
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